| Orateur(s) | Gal Binyamini - Weizmann Institute of Science,
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| Titre | Wilkie's conjecture for restricted elementary functions |
| Date | 13/01/2017 |
| Horaire | 11:00 à 12:30 |
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| Diffusion | |
| Résume | Let X be a set definable in some o-minimal structure. The Pila-Wilkie theorem (in its basic form) states that the number of rational points in the transcendental part of X grows sub-polynomially with the height of the points. The Wilkie conjecture stipulates that for sets definable in R_exp, one can sharpen this asymptotic to polylogarithmic.
I will describe a complex-analytic approach to the proof of the Pila-Wilkie theorem for subanalytic sets. I will then discuss how this approach leads to a proof of the “restricted Wilkie conjecture”, where we replace R_\exp by the structure generated by the restrictions of exp and sin to the unit interval (both parts are joint work with Dmitry Novikov). If time permits I will discuss possible generalizations and applications.
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| Salle | salle Pierre Grisvard, IHP |
| Adresse | IHP |
